Gagan Choudhury - Academia.edu (original) (raw)

Papers by Gagan Choudhury

Research paper thumbnail of Faster Link-State IGP Convergence and Improved Network Scalability and Stability

I t is desirable to have fast detection of failures followed by fast restoration and recovery in ... more I t is desirable to have fast detection of failures followed by fast restoration and recovery in data networks (IP, ATM, Frame relay, etc.) using link-state Interior Gateway Protocols (IGP). This requires faster hello exchanges (unless one relies on link level detection which is not always possible), fast flooding, and more frequent Shortest-Path-First calculations. However, through analysis and simulation we show that this compromises the scalability and stability of the network. This is mainly because Hello packets received at a router are indistinguishable from other packets and may experience long queueing delays during a sudden burst of many LSA (Link-State Advertisement) updates and cause the associated link to be declared down. At a later instant the link would recover. Both the failure and recovery generate fresh LSAs, in effect developing a feedback loop to sustain the LSA storm. We suggest that Hello and potentially some other IGP packets, such as acknowledgments, be marked explicitly so that they may be distinguished and queued separately from other IGP and data packets at the line rare and provided prioritized treatment. This allows significant reduction in IGP convergence time while maintaining network stability.

Bookmarks Related papers MentionsView impact

Research paper thumbnail of Network Design and Architectures for Highly Dynamic Next-Generation IP-Over-Optical Long Distance Networks

Journal of Lightwave Technology, 2000

Bookmarks Related papers MentionsView impact

Research paper thumbnail of Comments on "Exact results for nonsymmetric token ring systems

IEEE Transactions on Communications, 2000

Bookmarks Related papers MentionsView impact

Research paper thumbnail of PNNI routing congestion control

IEEE Communications Magazine, 2000

Bookmarks Related papers MentionsView impact

Research paper thumbnail of Special Issue on Converged Optical Networks

... K. Manousakis, K. Christodoulopoulos, E. Kamitsas, I. Tomkos, and EA Varvarigos 1866 ... D. H... more ... K. Manousakis, K. Christodoulopoulos, E. Kamitsas, I. Tomkos, and EA Varvarigos 1866 ... D. Hollenbeck and CD Cantrell 2140 CALLS FOR PAPERS JLT/MTT Joint Special Issue on Microwave Photonics . . . . . ...

Bookmarks Related papers MentionsView impact

Research paper thumbnail of Efficiently Providing Multiple Grades of Service with Protection Against Overloads in Shared Resources

AT&T Technical Journal, 1995

Bookmarks Related papers MentionsView impact

Research paper thumbnail of Two problems in internet reliability

ACM SIGMETRICS Performance Evaluation Review, 2004

This paper is motivated by two problems related to Internet reliability, where transient rather t... more This paper is motivated by two problems related to Internet reliability, where transient rather than traditional steady-state analysis is required. First, a failure and repair model for a router with active and redundant processors is considered. It is proved that the number of failed routers during given interval of time is asymptotically Poisson when the total number of routers is large and the parameter of the Poisson process is explicitly calculated. The second problem is related to reliability of a nationwide IP backbone. A situation, where operational links do not have enough spare capacity to carry additional traffic during the outage time, is referred to as bandwidth loss. We consider only one unidirectional backbone link and derive asymptotic aproximations for the expected bandwidth loss in the framework of generalized Erlang and Engset models when the total number of resource units and request arrival rates are proportionally large.

Bookmarks Related papers MentionsView impact

Research paper thumbnail of Resource-Sharing Models with State-Dependent Arrivals of Batches

Computations with Markov Chains, 1995

Bookmarks Related papers MentionsView impact

Research paper thumbnail of Concurrent ATM connection setup reducing need for VP provisioning

Proceedings of IEEE INFOCOM '96. Conference on Computer Communications, 1996

Bookmarks Related papers MentionsView impact

Research paper thumbnail of Improving stability and delay characteristics of multiple access systems employing ALOHA type channels

An approximate analysis of a flow control technique for improving stability and delay characteris... more An approximate analysis of a flow control technique for improving stability and delay characteristics of multiple access schemes employing collision type channels is presented. The technique allows users to enter two retransmission modes with differing retransmission rates. The condition under which such systems exhibit absolute stability and the minimum delay compatible with that condition have been determined. It is found that a significant improvement in delay is possible without having to sacrifice absolute stability.

Bookmarks Related papers MentionsView impact

Research paper thumbnail of Fluidanddiffusionlimitsforqueues Inslowlychangingenvironments

Bookmarks Related papers MentionsView impact

Research paper thumbnail of Computing transient and steady-state distributions in polling models by numerical transform inversion

We show that probability distributions of performance measures in a large class of polling models... more We show that probability distributions of performance measures in a large class of polling models can be effectively computed by numerically inverting transforms (generating functions and Laplace transforms). We develop new efficient iterative algorithms for computing the transform values and then use the Fourier-series method to perform the inversion. We also use this approach to compute moments. The algorithms apply to the transient behavior of stationary or nonstationary models as well as to the steady-state behavior of stationary models. Our main focus is on computing exact tail probabilities, but even for mean waiting times, our algorithm is faster than previous algorithms for large models. The computational complexity of our algorithm is O(Nα) for computing performance measures at one queue and O(N1+α) for computing performance measures at all queues, where N is the number of queues and α is typically between 0.6 and 0.8. We demonstrate effectiveness by computing performance m...

Bookmarks Related papers MentionsView impact

Research paper thumbnail of An Algorithm For Closed Queueing Networks Based On Numerical Transform Inversion

We propose a new algorithm for closed queueing networks and related product-form models based on ... more We propose a new algorithm for closed queueing networks and related product-form models based on numerical inversion of the generating function of the normalization constant (or partition function). It is known that the generating function of the normalization constant often has a remarkably simple form, but numerical inversion evidently has not been considered before. We also show that moments of steady-state distributions can be calculated directly by only performing two inversions. For closed queueing networks with p closed chains, the generating function is p dimensional. For these generating functions, the algorithm recursively performs p one-dimensional inversions. The required computation grows exponentially in the dimension, but we show that the dimension can often be reduced dramatically by exploiting special structure. Other key ingredients in the algorithm are scaling and the computation of large sums efficiently by Euler summation. Numerical examples indicate that this n...

Bookmarks Related papers MentionsView impact

Research paper thumbnail of Q²: A New Performance Analysis Tool Exploiting Numerical Transform Inversion

We describe a new tool that we are developing to help analyze the performance of emerging telecom... more We describe a new tool that we are developing to help analyze the performance of emerging telecommunication systems. These emerging systems include ATM, broadband, intelligent and wireless networks, each of which will support a wide variety of services and media. Our tool is distinguished from previous tools by exploiting numerical transform inversion. In this paper we describe three modules in the tool. These modules provide algorithms for obtaining the exact analytic solutions to: (i) resource-sharing models, (ii) BMAP/G/1 queueing models and (iii) polling models. Since the tool is based on analytical methods instead of simulation, it is relatively fast. The tool has a windowbased menu-driven interface and provides both graphical and numerical output. 1 Introduction In this paper we describe a new performance analysis tool that we are developing, called Q 2 , which exploits recent progress in numerical transform inversion. The tool has a user-friendly interface with window-based ...

Bookmarks Related papers MentionsView impact

Research paper thumbnail of on Teletraffic Theory and Engineering in memory of Fe lix ´ Pollaczek (1892-1981)

The steady-state waiting time in a stable GI/G/1 queue is equivalent to the maximum of a general ... more The steady-state waiting time in a stable GI/G/1 queue is equivalent to the maximum of a general random walk with negative drift. Thus, the distribution of the steady-state waiting time in the GI/G/1 queue is characterized by Spitzer’s (1956) formula. However, earlier, Pollaczek (1952) derived an equivalent contour-integral expression for the Laplace transform of the GI/G/1 steady-state waiting time. Since Spitzer’s formula is easier to understand probabilistically, it is better known today, but it is not so easy to apply directly except in special cases. In contrast, we show that it is easy to compute the GI/G/1 waiting-time distribution and its cumulants (and thus its moments) from Pollaczek’s formulas. For the waiting-time tail probabilities, we use numerical transform inversion, numerically integrating the Pollaczek contour integral to obtain the transform values. For the cumulants and the probability of having to wait, we directly integrate the Pollazcek contour integrals numer...

Bookmarks Related papers MentionsView impact

Research paper thumbnail of Asymptotic Analysis Of Tail Probabilities

Choudhury and Lucantoni recently developed an algorithm for calculating moments of a probability ... more Choudhury and Lucantoni recently developed an algorithm for calculating moments of a probability distribution by numerically inverting its moment generating function. They also showed that high-order moments can be used to calculate asymptotic parameters of the complementary cumulative distribution function when an asymptotic form is assumed, such as as x . Moment-based algorithms for computing asymptotic parameters are especially useful when the transforms are not available explicitly, as in models of busy periods or polling systems. Here we provide additional theoretical support for this moment-based algorithm for computing asymptotic parameters and new refined estimators for the case b 0. The new refined estimators converge much faster (as a function of moment order) than the previous estimators, which means that fewer moments are needed, thereby speeding up the algorithm. We also show how to compute all the parameters in a multi-term asymptote of the form F m . We identify condi...

Bookmarks Related papers MentionsView impact

Research paper thumbnail of Numerical solution of Mt /Gt /1 queues

Operations Research, 1993

Bookmarks Related papers MentionsView impact

Research paper thumbnail of <title>Evaluation of impact of backbone outages in IP networks</title>

Performance, Quality of Service, and Control of Next-Generation Communication Networks II, 2004

ABSTRACT Nationwide IP networks typically include nodes in major cities and the following element... more ABSTRACT Nationwide IP networks typically include nodes in major cities and the following elements: customer equipment, access routers, backbone routers, peering routers, access links connecting customer equipment to access routers, access routers to backbone routers, and backbone links interconnecting backbone routers. The part of this network consisting of backbone routers and related interconnecting links is referred to as the &quot;backbone&quot;. We develop a new approach for accurately computing the Availability measure of IP networks by directly simulating each type of backbone outage event and its impact on traffic loss. We use this approach to quantify availability improvement as a result of introducing various technological changes in the network such as IGP tuning, high availability router architecture, MPLS-TE and Fast Reroute. A situation, where operational backbone links do not have enough spare capacity to carry additional traffic during the outage time, is referred to as bandwidth loss. We concentrate on one unidirectional backbone link and derive asymptotic approximations for the expected bandwidth loss in the framework of generalized Erlang and Engset models when the total number of resource units and request arrival rates are proportionally large. Simulation results demonstrate good accuracy of the approximations.

Bookmarks Related papers MentionsView impact

Research paper thumbnail of Survivable IP link topology design in an IP-over-WDM architecture

2009 7th International Workshop on Design of Reliable Communication Networks, 2009

Bookmarks Related papers MentionsView impact

Research paper thumbnail of Numerical Transform Inversion to Analyze Teletraffic Models

Teletraffic Science and Engineering, 1994

Bookmarks Related papers MentionsView impact

Research paper thumbnail of Faster Link-State IGP Convergence and Improved Network Scalability and Stability

I t is desirable to have fast detection of failures followed by fast restoration and recovery in ... more I t is desirable to have fast detection of failures followed by fast restoration and recovery in data networks (IP, ATM, Frame relay, etc.) using link-state Interior Gateway Protocols (IGP). This requires faster hello exchanges (unless one relies on link level detection which is not always possible), fast flooding, and more frequent Shortest-Path-First calculations. However, through analysis and simulation we show that this compromises the scalability and stability of the network. This is mainly because Hello packets received at a router are indistinguishable from other packets and may experience long queueing delays during a sudden burst of many LSA (Link-State Advertisement) updates and cause the associated link to be declared down. At a later instant the link would recover. Both the failure and recovery generate fresh LSAs, in effect developing a feedback loop to sustain the LSA storm. We suggest that Hello and potentially some other IGP packets, such as acknowledgments, be marked explicitly so that they may be distinguished and queued separately from other IGP and data packets at the line rare and provided prioritized treatment. This allows significant reduction in IGP convergence time while maintaining network stability.

Bookmarks Related papers MentionsView impact

Research paper thumbnail of Network Design and Architectures for Highly Dynamic Next-Generation IP-Over-Optical Long Distance Networks

Journal of Lightwave Technology, 2000

Bookmarks Related papers MentionsView impact

Research paper thumbnail of Comments on "Exact results for nonsymmetric token ring systems

IEEE Transactions on Communications, 2000

Bookmarks Related papers MentionsView impact

Research paper thumbnail of PNNI routing congestion control

IEEE Communications Magazine, 2000

Bookmarks Related papers MentionsView impact

Research paper thumbnail of Special Issue on Converged Optical Networks

... K. Manousakis, K. Christodoulopoulos, E. Kamitsas, I. Tomkos, and EA Varvarigos 1866 ... D. H... more ... K. Manousakis, K. Christodoulopoulos, E. Kamitsas, I. Tomkos, and EA Varvarigos 1866 ... D. Hollenbeck and CD Cantrell 2140 CALLS FOR PAPERS JLT/MTT Joint Special Issue on Microwave Photonics . . . . . ...

Bookmarks Related papers MentionsView impact

Research paper thumbnail of Efficiently Providing Multiple Grades of Service with Protection Against Overloads in Shared Resources

AT&T Technical Journal, 1995

Bookmarks Related papers MentionsView impact

Research paper thumbnail of Two problems in internet reliability

ACM SIGMETRICS Performance Evaluation Review, 2004

This paper is motivated by two problems related to Internet reliability, where transient rather t... more This paper is motivated by two problems related to Internet reliability, where transient rather than traditional steady-state analysis is required. First, a failure and repair model for a router with active and redundant processors is considered. It is proved that the number of failed routers during given interval of time is asymptotically Poisson when the total number of routers is large and the parameter of the Poisson process is explicitly calculated. The second problem is related to reliability of a nationwide IP backbone. A situation, where operational links do not have enough spare capacity to carry additional traffic during the outage time, is referred to as bandwidth loss. We consider only one unidirectional backbone link and derive asymptotic aproximations for the expected bandwidth loss in the framework of generalized Erlang and Engset models when the total number of resource units and request arrival rates are proportionally large.

Bookmarks Related papers MentionsView impact

Research paper thumbnail of Resource-Sharing Models with State-Dependent Arrivals of Batches

Computations with Markov Chains, 1995

Bookmarks Related papers MentionsView impact

Research paper thumbnail of Concurrent ATM connection setup reducing need for VP provisioning

Proceedings of IEEE INFOCOM '96. Conference on Computer Communications, 1996

Bookmarks Related papers MentionsView impact

Research paper thumbnail of Improving stability and delay characteristics of multiple access systems employing ALOHA type channels

An approximate analysis of a flow control technique for improving stability and delay characteris... more An approximate analysis of a flow control technique for improving stability and delay characteristics of multiple access schemes employing collision type channels is presented. The technique allows users to enter two retransmission modes with differing retransmission rates. The condition under which such systems exhibit absolute stability and the minimum delay compatible with that condition have been determined. It is found that a significant improvement in delay is possible without having to sacrifice absolute stability.

Bookmarks Related papers MentionsView impact

Research paper thumbnail of Fluidanddiffusionlimitsforqueues Inslowlychangingenvironments

Bookmarks Related papers MentionsView impact

Research paper thumbnail of Computing transient and steady-state distributions in polling models by numerical transform inversion

We show that probability distributions of performance measures in a large class of polling models... more We show that probability distributions of performance measures in a large class of polling models can be effectively computed by numerically inverting transforms (generating functions and Laplace transforms). We develop new efficient iterative algorithms for computing the transform values and then use the Fourier-series method to perform the inversion. We also use this approach to compute moments. The algorithms apply to the transient behavior of stationary or nonstationary models as well as to the steady-state behavior of stationary models. Our main focus is on computing exact tail probabilities, but even for mean waiting times, our algorithm is faster than previous algorithms for large models. The computational complexity of our algorithm is O(Nα) for computing performance measures at one queue and O(N1+α) for computing performance measures at all queues, where N is the number of queues and α is typically between 0.6 and 0.8. We demonstrate effectiveness by computing performance m...

Bookmarks Related papers MentionsView impact

Research paper thumbnail of An Algorithm For Closed Queueing Networks Based On Numerical Transform Inversion

We propose a new algorithm for closed queueing networks and related product-form models based on ... more We propose a new algorithm for closed queueing networks and related product-form models based on numerical inversion of the generating function of the normalization constant (or partition function). It is known that the generating function of the normalization constant often has a remarkably simple form, but numerical inversion evidently has not been considered before. We also show that moments of steady-state distributions can be calculated directly by only performing two inversions. For closed queueing networks with p closed chains, the generating function is p dimensional. For these generating functions, the algorithm recursively performs p one-dimensional inversions. The required computation grows exponentially in the dimension, but we show that the dimension can often be reduced dramatically by exploiting special structure. Other key ingredients in the algorithm are scaling and the computation of large sums efficiently by Euler summation. Numerical examples indicate that this n...

Bookmarks Related papers MentionsView impact

Research paper thumbnail of Q²: A New Performance Analysis Tool Exploiting Numerical Transform Inversion

We describe a new tool that we are developing to help analyze the performance of emerging telecom... more We describe a new tool that we are developing to help analyze the performance of emerging telecommunication systems. These emerging systems include ATM, broadband, intelligent and wireless networks, each of which will support a wide variety of services and media. Our tool is distinguished from previous tools by exploiting numerical transform inversion. In this paper we describe three modules in the tool. These modules provide algorithms for obtaining the exact analytic solutions to: (i) resource-sharing models, (ii) BMAP/G/1 queueing models and (iii) polling models. Since the tool is based on analytical methods instead of simulation, it is relatively fast. The tool has a windowbased menu-driven interface and provides both graphical and numerical output. 1 Introduction In this paper we describe a new performance analysis tool that we are developing, called Q 2 , which exploits recent progress in numerical transform inversion. The tool has a user-friendly interface with window-based ...

Bookmarks Related papers MentionsView impact

Research paper thumbnail of on Teletraffic Theory and Engineering in memory of Fe lix ´ Pollaczek (1892-1981)

The steady-state waiting time in a stable GI/G/1 queue is equivalent to the maximum of a general ... more The steady-state waiting time in a stable GI/G/1 queue is equivalent to the maximum of a general random walk with negative drift. Thus, the distribution of the steady-state waiting time in the GI/G/1 queue is characterized by Spitzer’s (1956) formula. However, earlier, Pollaczek (1952) derived an equivalent contour-integral expression for the Laplace transform of the GI/G/1 steady-state waiting time. Since Spitzer’s formula is easier to understand probabilistically, it is better known today, but it is not so easy to apply directly except in special cases. In contrast, we show that it is easy to compute the GI/G/1 waiting-time distribution and its cumulants (and thus its moments) from Pollaczek’s formulas. For the waiting-time tail probabilities, we use numerical transform inversion, numerically integrating the Pollaczek contour integral to obtain the transform values. For the cumulants and the probability of having to wait, we directly integrate the Pollazcek contour integrals numer...

Bookmarks Related papers MentionsView impact

Research paper thumbnail of Asymptotic Analysis Of Tail Probabilities

Choudhury and Lucantoni recently developed an algorithm for calculating moments of a probability ... more Choudhury and Lucantoni recently developed an algorithm for calculating moments of a probability distribution by numerically inverting its moment generating function. They also showed that high-order moments can be used to calculate asymptotic parameters of the complementary cumulative distribution function when an asymptotic form is assumed, such as as x . Moment-based algorithms for computing asymptotic parameters are especially useful when the transforms are not available explicitly, as in models of busy periods or polling systems. Here we provide additional theoretical support for this moment-based algorithm for computing asymptotic parameters and new refined estimators for the case b 0. The new refined estimators converge much faster (as a function of moment order) than the previous estimators, which means that fewer moments are needed, thereby speeding up the algorithm. We also show how to compute all the parameters in a multi-term asymptote of the form F m . We identify condi...

Bookmarks Related papers MentionsView impact

Research paper thumbnail of Numerical solution of Mt /Gt /1 queues

Operations Research, 1993

Bookmarks Related papers MentionsView impact

Research paper thumbnail of <title>Evaluation of impact of backbone outages in IP networks</title>

Performance, Quality of Service, and Control of Next-Generation Communication Networks II, 2004

ABSTRACT Nationwide IP networks typically include nodes in major cities and the following element... more ABSTRACT Nationwide IP networks typically include nodes in major cities and the following elements: customer equipment, access routers, backbone routers, peering routers, access links connecting customer equipment to access routers, access routers to backbone routers, and backbone links interconnecting backbone routers. The part of this network consisting of backbone routers and related interconnecting links is referred to as the &quot;backbone&quot;. We develop a new approach for accurately computing the Availability measure of IP networks by directly simulating each type of backbone outage event and its impact on traffic loss. We use this approach to quantify availability improvement as a result of introducing various technological changes in the network such as IGP tuning, high availability router architecture, MPLS-TE and Fast Reroute. A situation, where operational backbone links do not have enough spare capacity to carry additional traffic during the outage time, is referred to as bandwidth loss. We concentrate on one unidirectional backbone link and derive asymptotic approximations for the expected bandwidth loss in the framework of generalized Erlang and Engset models when the total number of resource units and request arrival rates are proportionally large. Simulation results demonstrate good accuracy of the approximations.

Bookmarks Related papers MentionsView impact

Research paper thumbnail of Survivable IP link topology design in an IP-over-WDM architecture

2009 7th International Workshop on Design of Reliable Communication Networks, 2009

Bookmarks Related papers MentionsView impact

Research paper thumbnail of Numerical Transform Inversion to Analyze Teletraffic Models

Teletraffic Science and Engineering, 1994

Bookmarks Related papers MentionsView impact